General linear model: an effective tool for analysis of claim severity in motor third party liability insurance

The paper focuses on the analysis of claim severity in motor third party liability insurance under the general linear model. The general linear model combines the analyses of variance and regression and makes it possible to measure the influence of categorical factors as well as the numerical explanatory variables on the target variable. In the paper, simple, main and interaction effects of relevant factors have been quantified using estimated regression coefficients and least squares means. Statistical inferences about least-squares means are essential in creating tariff classes and uncovering the impact of categorical factors, so the authors used the LSMEANS, CONTRAST and ESTIMATE statements in the GLM procedure of the Statistical Analysis Software (SAS). The study was based on a set of anonymised data of an insurance company operating in Slovakia; however, because each insurance company has its own portfolio subject to changes over time, the results of this research will not apply to all insurance companies. In this context, the authors feel that what is most valuable in their work, is the demonstration of practical applications that could be used by actuaries to estimate both the claim severity and the claim frequency, and, consequently, to determine net premiums for motor insurance (regardless of whether for motor third party liability insurance or casco insurance.